Since the Miami airport is so close to the port, is it safe to book a 9:00 a.m. flight, if I am taking a cab?

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The Miami airport is one of my least favorite places to navigate. You may be able to make it (I doubt it) BUT any little thing from a delay in disembarkation, finding your luggage, hailing a cab, traffic (again, no picnic in Miami) to long security lines will cause you stress. Book a later flight and take it easy.